In a dry skillet, toast the guajillo and ancho chiles over medium heat until fragrant, about 2-3 minutes. Remove from heat and soak in hot water for 15 minutes.

Blend the soaked chiles with garlic, cumin, oregano, black pepper, and a little broth until smooth.

In a large pot, heat some oil over medium-high heat. Brown the beef and lamb on all sides, then remove from pot.

Add the chopped onion to the pot and sauté until translucent, about 5 minutes.

Return the meat to the pot, add the blended sauce, bay leaves, and remaining broth. Bring to a boil, then reduce heat and simmer for about 2 hours, or until the meat is tender.

Remove the meat, shred it, and return it to the pot. Serve hot with chopped cilantro, diced onion, lime wedges, and corn tortillas.